# Numerical Mesoscale Analysis of Textile Reinforced Concrete

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## Abstract

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## 1. Introduction

## 2. Construction of a Representative Volume Element for Textile Reinforced Concrete

#### 2.1. Geometry and Finite-Element Discretization

#### 2.2. Constitutive Modeling of Composite Constituents

#### 2.2.1. Textile Yarns

#### 2.2.2. Concrete

#### 2.2.3. Yarn–Concrete Interface

#### 2.3. Calibration of Model Parameters

#### 2.3.1. Identification of Yarn Material Parameters

#### 2.3.2. Identification of Concrete Material Parameters

#### 2.3.3. Identification of Interface Parameters

## 3. Numerical Material Testing

#### 3.1. Tensile Loading in Warp and Weft Direction

#### 3.2. Biaxial Tensile Loading

#### 3.3. In-Plane Shear Loading

## 4. Conclusions and Outlook

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Mesostructural unit cell (

**left**) and textile reinforcement with carbon filaments TUDALIT-BZT2- V.FRAAS adopted from [36] (

**right**).

**Figure 4.**Finite element mesh of two layered TRC-RVE with 4 × 143,492 linear tetrahedral elements, 4 × 3700 cohesive zone elements and 4 × 28,126 nodes.

**Figure 12.**Effective macroscopic stress–strain relation due to tensile loading in warp yarn direction with prescribed strain $\overline{\u03f5}=[{\overline{\u03f5}}_{xx},{\overline{\u03f5}}_{yy}=0,{\overline{\gamma}}_{xy}=0]$.

**Figure 13.**Experimental setup of TRC tensile test specimens according to [36], (photo by H. Michler (Institute of Concrete Structures, TU Dresden)).

**Figure 14.**Evolved effective mesoscopic damage distribution due to tensile loading in warp yarn direction with prescribed strain $\overline{\u03f5}=[{\overline{\u03f5}}_{xx},{\overline{\u03f5}}_{yy}=0,{\overline{\gamma}}_{xy}=0]$.

**Figure 15.**Effective macroscopic stress–strain relation due to tensile loading in weft yarn direction with prescribed strain $\overline{\u03f5}=[{\overline{\u03f5}}_{xx},{\overline{\u03f5}}_{yy}=0,{\overline{\gamma}}_{xy}=0]$.

**Figure 16.**Evolved effective mesoscopic damage distribution due to biaxial tensile loading with prescribed strain $\overline{\u03f5}=[{\overline{\u03f5}}_{xx}={\overline{\u03f5}}_{bt},{\overline{\u03f5}}_{yy}={\overline{\u03f5}}_{bt},{\overline{\gamma}}_{xy}=0]$.

**Figure 17.**Effective macroscopic stress–strain relation due to biaxial tensile loading with prescribed strain $\overline{\u03f5}=[{\overline{\u03f5}}_{xx}={\overline{\u03f5}}_{bt},{\overline{\u03f5}}_{yy}={\overline{\u03f5}}_{bt},{\overline{\gamma}}_{xy}=0]$.

**Figure 18.**Evolved effective mesoscopic damage distribution due to in-plane shear loading with prescribed strain $\overline{\u03f5}=[{\overline{\u03f5}}_{xx}=0,{\overline{\u03f5}}_{yy}=0,{\overline{\gamma}}_{xy}]$.

**Figure 19.**Effective macroscopic stress–strain relation due to in-plane shear loading with prescribed strain $\overline{\u03f5}=[{\overline{\u03f5}}_{xx}=0,{\overline{\u03f5}}_{yy}=0,{\overline{\gamma}}_{xy}]$.

Carbon Filaments | Lefasol VLT-1 Coating |
---|---|

${E}_{f\Vert}$ = 230,000 MPa | ${E}_{m}={G}_{m}(2+2{\nu}_{m})$ = 1802.9 MPa |

${E}_{f\perp}$ = 28,000 MPa | |

${G}_{f\perp \Vert}$ = 50,000 MPa | ${G}_{m}$ = 605 MPa |

${\nu}_{f\perp \Vert}$ = 0.23 | ${\nu}_{m}$ = 0.49 |

${\nu}_{f\perp \perp}$ = 0.259 |

E [GPa] | $\mathit{\nu}$ [-] | ${\mathit{f}}_{\mathit{uc}}$ [MPa] | ${\mathit{D}}_{\mathit{h}}$ [MPa${}^{2}$] | ${\mathit{R}}_{\mathit{t}}$ [-] | ${\mathit{\sigma}}_{\mathit{V}}^{\mathit{C}}$ [MPa] | R [-] | W [-] | ${\mathit{D}}_{\mathit{c}}$ [1/MPa] | e [-] | ${\mathit{A}}_{\mathit{s}}$ [-] | ${\mathit{\gamma}}_{\mathit{c}0}$ [-] | ${\mathit{\gamma}}_{\mathit{t}0}$ [-] | ${\mathit{\beta}}_{\mathit{t}}$ [-] | ${\mathit{\beta}}_{\mathit{c}}$ [-] | c [mm${}^{2}$] | m [-] |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

35 | $0.2$ | 105 | 72,500 | $0.5$ | $-80$ | 1 | $0.1325$ | $0.00125$ | $0.51$ | $1.9$ | $1.5\xb7{10}^{-4}$ | 0 | 4000 | 3500 | 1 | 2 |

${\mathit{\sigma}}_{0\mathit{I}}$ [MPa] | ${\mathit{G}}_{\mathit{cI}}$ [N/mm] | ${\mathit{\tau}}_{0\mathit{II}}$ [MPa] | ${\mathit{G}}_{\mathit{cII}}$ [N/mm] | $\mathit{\eta}$ [-] | $\mathit{\mu}$ [-] | ${\mathit{p}}_{0}$ [MPa] |
---|---|---|---|---|---|---|

$0.9$ | $0.05$ | $0.8$ | $0.3$ | $0.45$ | $0.6$ | $0.7$ |

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**MDPI and ACS Style**

Fuchs, A.; Curosu, I.; Kaliske, M. Numerical Mesoscale Analysis of Textile Reinforced Concrete. *Materials* **2020**, *13*, 3944.
https://doi.org/10.3390/ma13183944

**AMA Style**

Fuchs A, Curosu I, Kaliske M. Numerical Mesoscale Analysis of Textile Reinforced Concrete. *Materials*. 2020; 13(18):3944.
https://doi.org/10.3390/ma13183944

**Chicago/Turabian Style**

Fuchs, Alexander, Iurie Curosu, and Michael Kaliske. 2020. "Numerical Mesoscale Analysis of Textile Reinforced Concrete" *Materials* 13, no. 18: 3944.
https://doi.org/10.3390/ma13183944